Notes on the contact Ozsváth–Szabó invariants

Lisca, Paolo; Stipsicz, András I.

doi:10.2140/pjm.2006.228.277

Cited by 14 publications

(19 citation statements)

References 22 publications

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“…Thus Theorem 1 implies the following result. )) is independent of k and l. We are unable to say anything about the contactomorphism type of S 3 − (K n (k, l)), but in [15] it is shown that the Heegaard-Floer invariants of the S …”

Section: Examples Corollaries and Further Discussionmentioning

confidence: 84%

On contact surgery

Etnyre

2008

Proc. Amer. Math. Soc.

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Section: Examples Corollaries and Further Discussionmentioning

confidence: 84%

On contact surgery

Etnyre

2008

Proc. Amer. Math. Soc.

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“…Consider a Legendrian knot L with a Thurston-Bennequin invariant tb(L) > 0 in (S 3 , ξ std ). Let (M, ξ) denote the contact 3-manifold results from a +1-contact surgery along a positive stabilization S + (L) of the Legendrian knot L. (M, ξ) is overtwisted by [24] and also c.f by [21]. Since tb(S + (L)) ≥ 0 according to the previous Remark 5.4, sg(S + (L)) > 0.…”

Section: Final Remarks and Questionsmentioning

confidence: 97%

Invariants of Legendrian Knots from Open Book Decompositions

Onaran¹

2009

International Mathematics Research Notices

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In this note, we define a new invariant of a Legendrian knot in a contact 3manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structure ξ such that L sits on a page and the framings given by the contact structure and the page agree. We show any null-homologous loose knot in an overtwisted contact structure has support genus zero. To prove this, we show that any topological knot or link in any 3-manifold M sits on a page of a planar open book decomposition of M .1991 Mathematics Subject Classification. 57R17.

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“…We start with an open book adapted In this section we want to derive some applications of the theory developed in Section 4, Section 5 and Section 6. First to mention would be Proposition 7.1, which can also be derived using methods developed in [17]. There, Lisca and Stipsicz show that .C1/-contact surgery along stabilized Legendrian knots yield overtwisted contact manifolds, which implies the vanishing of the contact element.…”

Section: Implications To Contact Geometrymentioning

confidence: 97%